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Beliebt Rechnen >

3y^{''}-2y-y=2t^2-t-3e^{-3t}

Lösung

3 y^{^{''}} - 2 y - y = 2 t^{2} - t - 3 e^{- 3 t}

Lösung

y = c_{1} e^{t} + c_{2} e^{- t} + \frac{- 2 t ^{2} + t - 4}{3} - \frac{1}{8} e^{- 3 t}

Schritte zur Lösung

3 y^{''} (t) - 2 y - y = 2 t^{2} - t - 3 e^{- 3 t}

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{- t} + \frac{- 2 t ^{2} + t - 4}{3} - \frac{1}{8} e^{- 3 t}

y = c_{1} e^{t} + c_{2} e^{- t} + \frac{- 2 t ^{2} + t - 4}{3} - \frac{1}{8} e^{- 3 t}

Graph

Beliebte Beispiele

y^{''}-2y^'-15y=(6t+3tt+1)e^t

y^{^{''}} - 2 y^{^{'}} - 15 y = (6 t + 3 tt + 1) e^{t}

25y+12y^'+4y^{''}=-2

25 y + 12 y^{^{'}} + 4 y^{^{''}} = - 2

y^{'''}-y^'=4x^2+5x-2

y^{^{'''}} - y^{^{'}} = 4 x^{2} + 5 x - 2

y^{''}+3y^'+2y=1+4xe^{-3x}

y^{^{''}} + 3 y^{^{'}} + 2 y = 1 + 4 x e^{- 3 x}

y^{'''}+10y^{''}+25y^'=e^t

y^{^{'''}} + 10 y^{^{''}} + 25 y^{^{'}} = e^{t}